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＜電子ブック＞
The Beltrami Equation : A Geometric Approach / by Vladimir Gutlyanskii, Vladimir Ryazanov, Uri Srebro, Eduard Yakubov
(Developments in Mathematics. ISSN:2197795X ; 26)

版	1st ed. 2012.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2012
本文言語	英語
大きさ	XIV, 302 p : online resource
著者標目	*Gutlyanskii, Vladimir author Ryazanov, Vladimir author Srebro, Uri author Yakubov, Eduard author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Functions of complex variables FREE:Differential Equations FREE:Functions of a Complex Variable
一般注記	1. Introduction -- 2. Preliminaries -- 3. The Classical Beltrami Equation //μ//∞ < 1 -- 4. The Degenerate Case -- 5. BMO- and FMO-Quasiconformal Mappings -- 6. Ring Q-Homeomorphisms at Boundary Points -- 7. Strong Ring Solutions of Beltrami Equations -- 8. On the Dirichlet Problem for Beltrami Equations -- 9. On the Beltrami Equations with Two Characteristics -- 10. Alternating Beltrami Equation -- References -- Index The Beltrami Equation: A Geometric Approach will be particularly useful to many specialists in modern geometric analysis, quasiconformal mappings and extensions, beginning researchers, and graduate students with a year’s background in complex variables. This book covers the state-of-the art in the ongoing study of the Beltrami equation, the classical equation that has been studied for more than 100 years. Along with its rich history, the Beltrami equation plays a significant role in geometry, analysis, and physics.   The most important feature of this work concerns the unified geometric approach taken based on the modulus method that can be effectively applied to solving many problems in mathematical physics. Beautiful examples illustrate the relationship between mappings with bounded oscillation and those with finite oscillations.   Written by authors that are well-known specialists in this field, this monograph presents recent developments in the theory of Beltrami equations, studying a variety of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates, and boundary behavior of solutions to the Beltrami equations. It contains new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary HTTP:URL=https://doi.org/10.1007/978-1-4614-3191-6

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